The developer of an apartment building in The Bronx will be able to charge more renting it to the city for the homeless than by ­offering his 83 units to the public, documents show.

In a January filing seeking a property-tax break, Mark Stagg said he planned to charge private tenants an average of $641 per room in each apartment at 5731 Broadway in the Kingsbridge section.

A few months later, the de Blasio administration — desperate to find more space for the growing homeless population — agreed to rent the entire building to provide transitional housing to homeless families.

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Stagg is now proposing to charge up to $1,028 per room, according to an application for a 421-A property-tax exemption filed with the city Department of Housing Preservation and Development.

“There is no question that Stagg is clearly going to make more money renting the building to the city as a homeless shelter than had he done this deal as a responsible private landlord providing market-rental housing,” said Charles Moerdler, chair of the Land Use Committee of Community Board 8 and an ex-city housing commissioner.

“This is a very sweet deal for the developer and not a very good deal for the taxpayers.”

By dealing with the city, Stagg is also saving on marketing costs, is guaranteed a fixed rate of return and doesn’t have to worry about tenants not paying their rent.

The city Department of Homeless Services entered into a contract to pay the not-for-profit Praxis Housing Initiatives $5.3 million a year to operate the new family shelter, which includes social-service supports and security services.

Of that sum, Praxis is getting $2.4 million to cover rent payments to Stagg.

That comes to $200,000 a month, or an average of $2,409 per unit.

But Stagg insisted he’s not making a killing and is not charging the maximum rate.

“It’s not like we’re bringing in the Brink’s truck,” Stagg said. “This is not a windfall.”

He insisted his profit “is gong to be the same” as a homeless shelter as it would have been as a regular apartment building — because the two configurations included different tax breaks.

The initial proposal was for a 25-year tax break in which 80 percent of the apartments would have been market-rate and 20 percent “affordable.”

The new proposal to house homeless families seeks property-tax relief for 15 years.

Stagg claimed the city would end up paying an average of $1,869 for family apartment units, “which is actually below market rate.”